This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Cari is the lead architect for the city’s new aquarium. All of the tanks in the aquarium will be rectangular prisms where the side lengths are whole nu...
In this activity, learners explore scale by using building cubes to see how changing the length, width, and height of a three-dimensional object affects its surface area and its volume. Learners build bigger and bigger cubes to understand these scaling relationships.
Students analyze and begin to design a pyramid. Working in engineering teams, they perform calculations to determine the area of the pyramid base, stone block volumes, and the number of blocks required for their pyramid base. They make a scaled drawing of the pyramid using graph paper.
Students learn about Pascal's law, an important concept behind the engineering of dam and lock systems, such as the one that Thirsty County wants Splash Engineering to design for the Birdseye River (an ongoing hypothetical engineering scenario). Students observe the behavior of water in plastic water bottles spilling through holes punctured at different heights, seeing the distance water spurts from the holes, learning how water at a given depth exerts equal pressure in all directions, and how water at increasing depths is under increasing pressure.